Details

sample32.0ms

Algorithm

intervals

Results

6.0ms	202×	body	80	valid
5.0ms	35×	body	1280	valid
5.0ms	27×	body	2560	valid
2.0ms	86×	body	80	nan
1.0ms	12×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	2×	body	160	valid

simplify19.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	32	13
3	40	13
4	42	13
done	42	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

31.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms	(- (* b_2 b_2) (* a c))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

103 → 103

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	156	1821
1	368	1727
2	997	1611
3	3181	1595
done	5000	1594

prune242.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize11.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.7b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.3b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 187

Calls

4 calls:

17.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
40.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
27.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series522.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
174.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
218.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify995.0ms

Counts

199 → 199

Iterations

Useful iterations: done (989.0ms)

Iter	Nodes	Cost
0	304	5659
1	725	4896
2	2520	4718
done	5000	4716

prune512.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.3b

localize13.0ms

Local error

Found 4 expressions with local error:

6.4b	(/ (/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
6.7b	(/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
64×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
48×	`sqrt-prod`
38×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/l*`
14×	`sqrt-div`
12×	`associate-/r*` `difference-of-squares`
10×	`associate-/r/`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
6×	`pow1` `div-inv` `distribute-lft-out--`
4×	`add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate-/l/`

Counts

4 → 145

Calls

4 calls:

38.0ms	(/ (/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
21.0ms	(/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series1.1s

Counts

4 → 12

Calls

4 calls:

512.0ms	(/ (/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
497.0ms	(/ (* a c) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify813.0ms

Counts

157 → 157

Iterations

Useful iterations: done (808.0ms)

Iter	Nodes	Cost
0	260	3735
1	634	3358
2	2036	3174
done	5001	3170

prune474.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
20.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

53.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms	(- (* b_2 b_2) (* a c))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

101 → 101

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	175	1741
1	427	1541
2	1233	1375
3	4390	1349
done	5000	1348

prune229.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

regimes175.0ms

Accuracy

81.2% (4.8b remaining)

Error of 10.6b against oracle of 5.7b and baseline of 31.3b

bsearch80.0ms

Steps

Iters	Range		Point
8	2.1878188410446244e+107	3.8616146939177386e+111	3.6627135292415903e+111
8	-4.854151311909829e-126	-9.294658666337375e-130	-4.7828589349284326e-126

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	33
1	30	33
done	30	33

end0.0ms

sample991.0ms

Algorithm

intervals

Results

211.0ms	1110×	body	2560	valid
186.0ms	5789×	body	80	valid
135.0ms	885×	body	1280	valid
94.0ms	2997×	body	80	nan
55.0ms	449×	body	640	valid
28.0ms	256×	body	320	valid
24.0ms	102×	body	5120	valid
10.0ms	124×	body	160	valid